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Question

A spherical conducting shell of inner radius $$r_{1}$$ and outer radius $$r_{2}$$ has a charge $$'Q'$$. A charge $$'q'$$ is placed at the centre of the shell.
(a) What is the surface charge density on the (i) inner surface, (ii) outer surface of the shell?
(b) Write the expression for the electric field at a point $$x > r_{2}$$ from the centre of the shell.


Solution

(a) Charge $$Q$$ resides on outer surface of spherical conducting shell. Due to charge $$q$$ placed at centre, charge induced on inner surface is $$-q$$ and on outer surface it is $$+q$$. So, total charge on inner surface $$-q$$ and on outer surface it is $$Q + q$$.
Surface charge density on inner surface $$= -\dfrac {q}{4\pi r_{1}^{2}}$$
Surface charge density on outer surface $$= \dfrac {Q + q}{4\pi r_{2}^{2}}$$
(b) For example points, whole charge acts at centre, so electric field at distance $$x > r^{2}, E(x) = \dfrac {1}{4\pi \epsilon_{0}} \dfrac {Q + q}{x^{2}}$$.
1663445_1571852_ans_a2534f36cc4b4728b439ecc0a3fe4b0c.png

Physics

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